Billie Holiday weaves, discombobulated, onto the stage. Sozzled, maybe. High, quite possibly. She shakes her head, bunches her fists, peers out into a Philadelphia club. “Philly’s always been the rat’s arse for me,” she growls. Lanie Robertson’s 1986 play is inspired by stories of Holiday working small clubs towards the end of her life, when singing was the only thing that kept her straight, just about. Played by the Broadway darling Audra McDonald, Holiday lobs aching melodies into an unstoppable monologue, ignoring her pianist’s frown as she rambles through grievances and regrets. Inevitably, a staid West End audience is more Rotary Club than Cotton Club — an awkwardness that sharpens the sense we’re gawping at an…